Pinning adaptive synchronization of a general complex dynamical network

Zhou, Jin; Lu, Jun-an; Lü, Jinhu

doi:10.1016/j.automatica.2007.08.016

Cited by 535 publications

(258 citation statements)

References 22 publications

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“…As has been shown in Refs. [18][19][20]23, and 24, the coupling matrix G and the coupling strength c directly affect the controllability of the network; these parameters also affect the detailed selection, as follows from the above description. Thus, it is difficult to decide on the selection strategy.…”

Section: Preliminariesmentioning

confidence: 99%

“…[6][7][8][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In particular, the study on controlling the dynamics of a network and guiding it to a desired state, such as, an equilibrium point or a periodic orbit of the network has become an interesting and important direction in this research field. 7,[18][19][20][22][23][24]26,27 It has been revealed that, in the process of controlling various networks, feedback control serves as a simple and effective approach for stabilization and synchronization. However, it is widely believed that it is impossible to add controllers to all nodes.…”

Section: Introductionmentioning

confidence: 99%

“…To reduce the control cost, some feedback injections may be added to a fraction of network nodes, which is known as pinning control. [17][18][19][20][22][23][24]26,27,33 In Ref. 17, pinning control of spatiotemporal chaos was discussed.…”

Section: Introductionmentioning

confidence: 99%

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Pinning control of fractional-order weighted complex networks

Tang

Wang

Fang

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

129

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In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated. A surprising finding is that the fractional-order complex networks can stabilize itself by reducing the fractional-order q without pinning any node. Second, numerical algorithms for fractional-order complex networks are introduced in detail. Finally, numerical simulations in scale-free complex networks are provided to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger overall coupling strength c, the more capacity that the pinning scheme may possess to enhance the control performance of fractional-order complex networks. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3068350͔Recently, fractional-order differential systems have been widely investigated due to their potential applications in viscoelasticity, dielectric polarization, quantum evolution of complex systems, and many other fields. On the other hand, research of complex networks has triggered tremendous interest during the past decade. Most studies to date have concerned integer-order complex networks. In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The fractional-order complex networks generalize wellstudied integer-order complex networks. Some local stability properties of such pinned fractional-order networks are derived and the valid stability regions are estimated by utilizing the eigenvalue analysis and fractional-order stability theory. A surprising finding that the fractional-order networks can stabilize itself by reducing the fractional-order q without pinning any node is presented. The numerical algorithms for fractional-order networks are also presented. In the end, computer simulations in scale-free networks are given to show that the smaller fractional-order q, the larger control gain matrix D, the larger tunable weight parameter ␤, the larger coupling strength c, the more capacity that the pinning strategy can possess to accelerate the control rate of fractional-order networks.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pinning control of fractional-order weighted complex networks

Tang

Wang

Fang

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

129

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“…Yet, in practice we do not always have access to the global network topology. Given this limitation, recently adaptive control has been proposed for pinning synchronization, in which case a controller adapts to a controlled system with parameters that vary in time, or are initially uncertain, without requiring a detailed knowledge of the global network topology (DeLellis et al, 2011(DeLellis et al, , 2010Wang et al, 2008;Wang and Slotine, 2006;Wang et al, 2010;Zhou et al, 2008). As we discuss next, many different strategies have been designed to tailor the control gains, coupling gains, or to rewire the network topology to ensure pinning synchronizability.…”

Section: Adaptive Pinning Controlmentioning

confidence: 99%

“…(i) Adaptation of control gains: To adapt the control gain κ i (101), representing the ratio between the pinning function and output function, we choose the control input u i (t) = −δ i κ i (t)(x i (t) − s), and the control gains as Zhou et al, 2008) …”

Section: Adaptive Pinning Controlmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

543

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Bibliography

2016

Distributed Cooperative Control of Multi‐agent Systems

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Pinning adaptive synchronization of a general complex dynamical network

Cited by 535 publications

References 22 publications

Pinning control of fractional-order weighted complex networks

Pinning control of fractional-order weighted complex networks

Control principles of complex systems

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